CEdward
ScottTargetTestPrep
GMATinsight
In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???
A) 4
B) 6
C) 12
D) 16
E) 24
Source:
https://www.GMATinsight.comThe number of ways to pick 3 walls from 4 is 4C3 = 4. Once 3 walls are picked, the number of ways to mount the portraits onto the walls is 3! = 6. Therefore, there are a total of 4 x 6 = 24 ways to mount 3 portraits on 3 of the four walls inside a room.
Answer: E
Hi can someone help on this one? Why is it that 3 different portraits can be mounted on 3 walls 3! ways?
How come it's not 6! / 3! x 3! = 20 ways?
ppp ||| <---- 3 portraits and 3 divisors so 6!/3! x 3!
I guess the idea here is that there can be a maximum of one portrait per wall...
Response:As a matter of fact, you are correct; the question should have said “one painting per wall.” However, your answer of 20 is not the correct answer for that scenario (unless the paintings are identical, which we know is not the case). If we can mount more than one painting per wall, the number of ways should increase. If that was the case, you would solve “prq |||” instead of “ppp |||”.